Preheat oven to 350°F. Spray three 8" cake pans with nonstick cooking spray and line the bottom with parchment paper. Set aside.
In a large bowl, combine brown sugar, canola oil, applesauce and eggs. Beat with an electric mixer until smooth. Add vanilla extract and beat until combined.
In a separate bowl, combine flour, baking powder, baking soda, spices and salt. Whisk until blended.
Add dry ingredients to wet ingredient bowl. Beat with electric mixer until just combined. Fold in sour cream until well blended.
Divide batter evenly between 3 prepared cake pans. Bake for 40 minutes, or until toothpick pocked into the centre comes out clean.
Once cakes are baked, remove from oven and allow to cool 5-10 minutes before transferring to a cooling rack.
For The Frosting
While the cakes are baking, begin the frosting. In a medium saucepan, add butter over low/medium heat. Allow butter to bubble until it begins to brown, about 3-4 minutes. Remove from the heat and transfer to a heatproof bowl. Allow to cool completely before moving to next step.
In a large mixing bowl, combine (cooled) browned butter, cream cheese, confectioners' sugar, vanilla extract and cinnamon. Beat with an electric mixer, adding 1-2Tbsp of milk to soften, until smooth and fluffy.
Level the top of each cake layer with a sharp serrated knife.
Add a layer of frosting between each layer. Cover cake and chill for approximately 30 minutes.
Once chilled, frost cake with remaining frosting as desired.